A wire of length L and radius r is rigidly fixed at one end. On stretching the other end of the wire with a force F, the increase in its length is l. If another wire of same material but of length 2L and radius 2r is stretched with a force of 2F, the increase in its length will be
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$l = \frac{\mathrm{FL}}{\mathrm{AY}} = \frac{\mathrm{FL}}{\pi r^{2} Y} \therefore l \propto \frac{\mathrm{FL}}{r^{2}} \left( Y = \text{constant} \right)$ $\therefore \frac{l_{2}}{l_{1}} = \frac{F_{2}}{F_{1}} \times \frac{L_{2}}{L_{1}} \left( \frac{r_{1}}{r_{2}} \right)^{2} = 2 \times 2 \times \left( \frac{1}{2} \right)^{2} = 1$ $\therefore l_{2} = l_{1}$ i.e. increment in its length will be l.
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